4.17.9 \(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\)

ODE
\[ -2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
Change of variable

Mathematica
cpu = 599.998 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.403 (sec), leaf count = 27

\[ \left \{ y \relax (x ) ={\frac {{\it \_C1}\, \left (a{x}^{2}-{\it \_C1} \right ) }{a}},y \relax (x ) ={\frac {a{x}^{4}}{4}} \right \} \] Mathematica raw input

DSolve[4*a*x^2*y[x] - 2*a*x^3*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x)^2-2*a*x^3*diff(y(x),x)+4*a*x^2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = 1/4*a*x^4, y(x) = _C1*(a*x^2-_C1)/a